Abstract

URRUTIA-GALICIA, J.L.; ALCERRECA-HUERTA, J.C.  and  ORDAZ-ALCANTARA, M.A.. Linear programming in covariant and contravariant manifolds: A physical and mathematical perspective. Ing. invest. y tecnol. [online]. 2008, vol.9, n.3, pp.185-204. ISSN 2594-0732.

In this paper a new optimization method is presented. The theoretical back ground is different to that used presently as in the case of the "Simplex Method". The presentation is based on the use of the covariant and contravariant spaces, both being biorthogonal spaces, al low a visualization of the optimization problem from a physical as well as mathematical points of view. The obtained result provides the best approximation according to the data provided in the constraints of the problem, which are visualized like vectors and not like straight lines, planes or hyperplanes. Also, in this new method the error generated between the approximation and the objective vectors can be measured, which allows to observe and prove the accuracy of the proposed solution.

Keywords : Optimization methods; covariant and contravariant spaces -vs- simplex method; hyperplane rotation; convergence; exact solution.

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